Self Numbers

Problem Description

In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), .... For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence
33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ...

The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.


Write a program to output all positive self-numbers less than or equal 1000000 in increasing order, one per line.

 

Sample Output

 

Source

Mid-Central USA 1998

尼玛，太简单了，之间就水过去了.....

代码：

 1 #include<cstdio> 2 #include<cstring> 3 #define maxn 1000001 4 /*求个位数之和*/ 5 int work(int n) 6 { 7     int sum=0; 8     while(n>0){ 9       sum+=n%10;10       n/=10;11     }12     return sum;13 }14 bool ans[maxn];15 int main(){16     int pos;17     //freopen("test.out","w",stdout);18     memset(ans,0,sizeof(ans));19     for(int i=1;i<maxn;i++){20         pos=i+work(i);21         if(pos<=1000000&&!ans[pos]) ans[pos]=1;22     }23     for(int i=1;i<maxn;i++){24         if(!ans[i])printf("%d\n",i);25     }26 return 0;27 }